Mathematical modelling reveals cellular dynamics within tumour spheroids
Mathematical modelling reveals cellular dynamics within tumour spheroids
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DOI：
10.1371/journal.pcbi.1007961
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发表时间：
2020-08-01
影响因子：
4.3
通讯作者：
Byrne, Helen M.
中科院分区：
文献类型：
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作者：
Bull, Joshua A.;Mech, Franziska;Byrne, Helen M.
肿瘤球状体是一种实验性测定，用于确定不同癌细胞系的动力学和对治疗的反应。先前的实验已经证明，肿瘤细胞增殖到球体边缘的局部化（由于营养物从周围介质扩散形成的梯度）导致细胞从增殖边缘被推向营养缺乏的坏死核心。这种运动允许惰性颗粒渗入肿瘤球状体。我们使用一个混合的基于代理的模型来重现这些数据。我们进一步展示了如何从单个微珠轨迹的数据可以用来推断模拟肿瘤球体的组成，并估计模型参数有关的肿瘤细胞增殖率和它们对缺氧的反应。由于这些测量是可能的，使用现代成像技术，这可能会激发新的实验中，球状体的组成可以推断通过观察惰性particle.Tumour球状体的被动infiltration被广泛用作anin vitroassay为特征的动态和不同的癌细胞系的治疗反应。它们的流行主要是由于球体生长的可重复方式：营养物质和氧气从周围培养基中扩散，以及肿瘤细胞对其的消耗，导致增殖局限于球体边界。随着球体的生长，球体中心的细胞可能变得缺氧并死亡，形成坏死的核心。由肿瘤细胞增殖和死亡的局部化产生的压力产生肿瘤细胞从球体边缘向其核心的细胞流动。Dorie等人的实验表明，通过将微珠添加到肿瘤球状体的表面并观察随时间的分布，该流动导致惰性微球通过从球状体表面的平流渗透到肿瘤球状体中。我们使用一个非格子混合代理为基础的模型来重新评估这些实验，并建立微球产生的时空数据可以用来推断与肿瘤球体，他们渗透的动力学参数的程度。这些参数的变化，如肿瘤细胞增殖率或对缺氧的敏感性，可以产生具有相似的整体生长动力学但不同内部组成（肿瘤增殖、缺氧/静止和坏死/营养缺乏的比例）的球状体。我们使用该模型表明Dorieet al.进行的实验类型可用于推断与肿瘤细胞系相关的球体组成和参数，例如它们对缺氧的敏感性或平均增殖速率，并注意到这些观察结果不能在微珠浸润肿瘤球体的先前连续模型中进行，因为它们依赖于解析单个微珠的轨迹。
Author summary Tumour spheroids are an experimental assay used to characterise the dynamics and response to treatment of different cancer cell lines. Previous experiments have demonstrated that the localisation of tumour cell proliferation to the spheroid edge (due to the gradient formed by nutrient diffusing from the surrounding medium) causes cells to be pushed from the proliferative rim towards the nutrient-deficient necrotic core. This movement allows inert particles to infiltrate tumour spheroids. We use a hybrid agent-based model to reproduce this data. We show further how data from individual microbead trajectories can be used to infer the composition of simulated tumour spheroids, and to estimate model parameters pertaining to tumour cell proliferation rates and their responses to hypoxia. Since these measurements are possible using modern imaging techniques, this could motivate new experiments in which spheroid composition could be inferred by observing passive infiltration of inert particles.Tumour spheroids are widely used as anin vitroassay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorieet al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to re-assess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorieet al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.